In this book the main problems related to the construction of an Earth-Model are presented and discussed. The first three chapters are dedicated to the classical methods that can be used to build numerical models, in particular, the author proposes:- some of the classical modeling techniques used in Computer Aided Design (CAD) to model surfaces and their inadequacy for modeling complex geological objects, in particular:- classical interpolation techniques used to model surfaces;- topological models used to describe the connections between surfaces and volumes;- an overview of geomodeling methods dedicated to the discrete modeling of geological objects, in particular:- the Discrete-Smooth-Interpolation method (DSI);- meshing techniques to model surfaces and grids;- a presentation of the classical ?Shared-Earth-Model? (SEM) paradigm consisting in a Structural-Model (SM) plus a Property-Model (PM): SEM = SM + PM- a discussion concerning the problems raised by the (in) compatibility between the Structural-Model (SM) and the Property-Model (PM).